Answer: 3.5
Step-by-step explanation:
ΔATM ≅ ΔCTM by ASA, therefore AM = CM by CPCTC
Similarly, ΔBTM ≅ ΔDTM by ASA, therefore BM = DM
By the Segment Addition Postulate, BA + AM = BM, MC + CD = MD
Since AM ≅ CM and BM ≅ DM, then by substitution we know that BA ≅ CD
By the segment addition postulate, BA + AM + MC + CD = BD
It is given that AM = 5 and BD = 17.
We have shown (above) that AM = MC and BA = CD,
so use substitution to solve for CD:
BA + AM + MC + CD = BD
CD + 5 + 5 + CD = 17
10 + 2CD = 17
2CD = 7
CD = 3.5
